Acta mathematica scientia,Series A ›› 2001, Vol. 21 ›› Issue (zk): 584-590.
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GUAN Yan-Hui
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Abstract:
１９８６年，Ｐ．Ｌｉ与丘成桐给出了带凸边界的紧黎曼流形上关于热核的一个Ｈａｒｎａｃｋ不等式（可参看［６］），而该文的目的正是将他们的工作推广到可能带非凸边界的紧黎曼流形上．
Key words: 热核, 黎曼流形, Ｈａｒｎａｃｋ不等式
CLC Number:
GUAN Yan-Hui. Heat Kernel Riemannian Manifold, Harnack Inequality[J].Acta mathematica scientia,Series A, 2001, 21(zk): 584-590.
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１ ＣｈｏｗＢ．ＬｅｃｔｕｒｅｎｏｔｅｓｏｎＨａｒｎａｃｋｉｎｅｑｕａｌｉｔｉｅｓｆｏｒｃｕｒｖａｔｕｒｅｆｌｏｗｓ．１９９７ ２ ＲｏｇｅｒＣｈｅｎ．Ｎｅｕｍａｎｎｅｉｇｅｎｖａｌｕｅｅｓｔｉｍａｔｅｏｎａｃｏｍｐａｃｔｒｉｅｍａｎｎｉａｎ ｍａｎｉｆｏｌｄ．ＰｒｏｃｅｅｄｉｎｇｓｏｆｔｈｅＡｍｅｒｉｃａｎ ＭａｔｈｅｍａｔｉｃａｌＳｏｃｉｅｔｙ，１９９０，１０８（４）：９６１－９７０ ３ ＨａｍｉｌｔｏｎＲ．ＴｈｅＨａｒｎａｃｋｅｓｔｉｍａｔｅｆｏｒｔｈｅＲｉｃｃｉｆｌｏｗ．ＪＤｉｆｆＧｅｏｍ，１９９３，３７：２２５－２４３ ４ ＨａｍｉｌｔｏｎＲ．Ｈａｒｎａｃｋｅｓｔｉｍａｔｅｆｏｒｔｈｅｍｅａｎｃｕｒｖａｔｕｒｅｆｌｏｗ．ＪＤｉｆｆＧｅｏｍ，１９９５，４１：２１５－２２６ ５ ＬｉＰ．Ｌｅｃｔｕｒｅｎｏｔｅｓｏｎｇｅｏｍｅｔｒｉｃａｎａｌｙｓｉｓ．１９９６ ６ ＬｉＰ，ＹａｕＳＴ．ＯｎｔｈｅｐａｒａｂｏｌｉｃｋｅｒｎｅｌｏｆｔｈｅＳｃｈｒ¨ ｏｄｉｎｇｅｒｏｐｅｒａｔｏｒ．ＡｃｔａＭａｔｈ，１９８６，１５６：１５３－２０１ ７ ＹａｕＳＴ．ＬｅｃｔｕｒｅｎｏｔｅｓｏｎＮｏｎｌｉｎｅａｒｓｃａｌａｒｅｑｕａｔｉｏｎ． ８ 丘成桐，孙理察．微分几何．北京：科学出版社，１９８８ ９ ＷａｒｎｅｒＦ Ｗ．ＥｘｔｅｎｓｉｏｎｏｆｔｈｅＲａｕｃｈｃｏｍｐａｒｉｓｏｎｔｈｅｏｒｅｍｔｏｓｕｂｍａｎｉｆｏｌｄ．ＴｒａｎｓＡｍｅｒＭａｔｈＳｏｃ，１９６６，１２２：３４１－３５６
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